Problem: Simplify the following expression: $ t = \dfrac{4z - 9}{-2z} - \dfrac{-4}{7} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{4z - 9}{-2z} \times \dfrac{7}{7} = \dfrac{28z - 63}{-14z} $ Multiply the second expression by $\dfrac{-2z}{-2z}$ $ \dfrac{-4}{7} \times \dfrac{-2z}{-2z} = \dfrac{8z}{-14z} $ Therefore $ t = \dfrac{28z - 63}{-14z} - \dfrac{8z}{-14z} $ Now the expressions have the same denominator we can simply subtract the numerators: $t = \dfrac{28z - 63 - 8z }{-14z} $ Distribute the negative sign: $t = \dfrac{28z - 63 - 8z}{-14z}$ $t = \dfrac{20z - 63}{-14z}$ Simplify the expression by dividing the numerator and denominator by -1: $t = \dfrac{-20z + 63}{14z}$